And, I've heard two stories about how this 'tradition' was started: one, that it was said to represent coalminers but the second, was that poor people blackened their face so that they could dance for money, undetected
It depends what part of the country the tradition comes from.
Basic Morris Dancing (hobby horse, jester, various characters, bells, sticks, ribbons, country style reels and jigs etc) is really old and universal across the British Isles.
Blacking up was associated with rural areas and night time poaching. See the Waltham Act 1723, also known as the Black Act, which made the crime of being disguised to poach at night, AKA 'going equipped', a capital offence. The theory is that blacking up became part of Morris dancing, during the day at a festival, as a way of mocking what was seen as an unjust law but without the chance of being arrested for it. They are agricultural labourers taunting the lord of the manor type of thing.
Also in coal mining areas, they had their own versions of Morris dancing and also some blacked up. This would be more like a display of solidarity, as these communities were very tight knit and later became very unionised. Miners have always been very proud of the job they do and very much depended on each for safety.